Formulating the Process-industry Load

Oil Boiler Formulation

The oil-boiler fuel consumption during interval k, denoted with Fk (ton/hour), is rep-

resented by a linear function of the thermal energy produced during the hour [43], as follows: Fk= A1Vk+ B1· T Pkob (6.8) Fmin· Vk ≤ Fk ≤ Fmax· Vk (6.9) Costob = (Mob_{+ ρ}oil₎X k Fk (6.10)

whereA1andB1are the coefficients of the linear functions which are obtained from the

oil-boiler technical performance data;T Pob

k (MW) is the oil-boiler thermal power during

intervalk; FminandFmaxare fuel consumption limits of the oil-boiler, Costob is the total operation cost of the oil-boiler over the 24-hour planning period; Mob _{is the operation} and maintenance (O&M) costs of the oil-boiler; and ρoil _{is the contracted price of oil} which remains constant over the planning period. Vk is a binary variable representing

oil-boiler status at the planning intervalk that can be defined as follows:

Vk=

  

1 if the oil-boiler is on.

0 if the oil-boiler is off. (6.11)

Gas Engine Formulation

Similarly, the gas engine fuel consumption during intervalk, denoted by Gk(km3(N)/h)2,

is represented by a linear function of the thermal and electrical energy produced during 2_{Kilo normal cubic meter of natural gas per hour.}

that interval [43], as follows: Gk = A2 · Wk+ B2· T Pkge (6.12) Gk = A3 · Wk+ B3· EPkge (6.13) Gmin· Wk ≤ Gk ≤ Gmax· Wk (6.14) Costge = MgeX k EP_kge+ ρngX k Gk (6.15)

where A2, B2, A3, and B3 are the linear coefficients which are obtained from the gas

engine technical performance data;T P_kge(MW) is the gas engine thermal power during interval k, EP_kge (MW) is the gas engine electrical power during interval k; Gmin and

Gmax are fuel consumption limits of the gas engine; Mge represents the O&M costs of the gas engine; and ρng _{is the fixed natural gas price. The total costs associated with} the gas engine operation, i.e., Costge, is formulated as a function of the electrical energy produced and the amount of fuel consumed. Wk is a binary variable representing the

status of the gas engine during the intervalk as follows:

Wk =

  

1 if the gas engine is on.

0 if the gas engine is off. (6.16)

Gas Engine Carbon Dioxide Emissions

It is assumed that the process-industry load has to maintain its CO2 emissions, result-

ing from electricity generation, below a certain specified limit ofEmCap (ton/day), as

follows:

Emge_·X

k

EP_kge ≤ EmCap (6.17)

whereEmge_{is theCO}

2 emission of the gas engine per MWh of electrical energy gener-

Electricity Market Transaction Cost

The cost of the net electricity transaction with the market can be presented as:

Costmar= (1 + α)Xρk· Ekimp−

X

ρk· Ekexp (6.18)

whereE_kimp(MW) andE_kexp(MW) are the electrical energy imported and exported from/to the market during the planning interval k, respectively, and Costmar _{is the net cost of} electricity transaction with the market. Observe that there is an extra uplift charge, rep- resented by α, associated with the energy imported from the market to account for the

network charges and other regulated fees; for example, a 30% uplift charge on top of total electricity costs typically applies to Ontario electricity consumers.

Energy Balance

The thermal demand must be met at all hours by the thermal energy produced either by the oil-boiler or by the gas engine or both. The electrical demand must also be met either by the electricity purchased from the market or the electricity produced by the gas engine or a combination of the two. Hence, the energy balance constraints can be written as follows: T Pob k + T P ge k = T Dk (6.19) E_kimp+ Ekl = EDk (6.20) EP_kge = Ekl + E exp k (6.21)

whereT Dk (MW) andEDk (MW) are the hourly thermal and electrical loads, respec-

tively. El

k (MW) is the electric power from the gas engine supplying the local demand

Objective Function

The optimization objective is to minimize the total expected energy cost over a 24-hour planning period while meeting all the system constraints defined in (6.8) to (6.21). Thus:

min

k E[Cost

pil_{|I] = Cost}ob_{+ Cost}ge_{+ (1 + α)}X ˆ

ρk· Ekimp−

X ˆ

ρk· Ekexp (6.22)

whereE[Costpil_{|I] is the expected total energy cost of the process-industry load.}

The above optimization model is a Linear Mixed-Integer Programming (LMIP) prob- lem and is solved using the well-known CPLEX solver in the GAMS programming en- vironment [89].

After the actual electricity market prices are released, the final energy cost of the process-industry load, denoted byCostˆ pilhere, can be found as:

ˆ

Costpil = ˆCostob+ ˆCostge+ (1 + α)Xρa k· ˆE imp k − X ρa k· ˆE exp k (6.23)

where ˆE_kimpand ˆE_kexpare the scheduled energy import and export from and to the market by solving (6.22), andCostˆ obandCostˆ ge are the costs of the oil boiler and the gas engine associated with the solution of (6.22). Note that Costˆ ob and Costˆ ge do not depend on the electricity market prices, and hence will take the same values as those found from solving (6.22).